Displaying similar documents to “Ascent and descent for sets of operators”

Diagonals of Self-adjoint Operators with Finite Spectrum

Marcin Bownik, John Jasper (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).

Notes on q-deformed operators

Schôichi Ôta, Franciszek Hugon Szafraniec (2004)

Studia Mathematica

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The paper concerns operators of deformed structure like q-normal and q-hyponormal operators with the deformation parameter q being a positive number different from 1. In particular, an example of a q-hyponormal operator with empty spectrum is given, and q-hyponormality is characterized in terms of some operator inequalities.

On the generalized Kato spectrum

Benharrat, Mohammed, Messirdi, Bekkai (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 47A10. We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory.

Polaroid type operators and compact perturbations

Chun Guang Li, Ting Ting Zhou (2014)

Studia Mathematica

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A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property...

The Słodkowski spectra and higher Shilov boundaries

Vladimír Müller (1993)

Studia Mathematica

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We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.

Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.